This invention relates to a method and apparatus for the control of the shape of a planar structure, and in particular to an instrument in which thermal gradients are used to control the shape of the surface of a diffraction crystal.
It is well known in the prior art that photons may be focused by specular reflection from mirror surfaces and by diffraction from crystallographic planes. Instruments incorporating these features include spectrometers, medical devices used to focus or increase the intensity of a beam for treatment purposes, satellite telescopes used for focusing parallel beams of photons such as x-rays and gamma rays from deep space, and devices useful for research purposes where beams of photons or particles are directed against samples to determine particular characteristics of the samples.
Mirrors have been used in these instruments to direct and to focus beams of photons because they can be fabricated in various curvatures, thereby providing precise control over the direction and shape of the beams. In instruments where complex focusing is required, mirrors can be fabricated as both cylindrical and ellipsoidal surfaces and can be used to obtain both single and double focusing.
However, mirrors can be used conveniently only in instruments utilizing low energy photon beams. Mirrors work well for energies below 10 keV and are useful for energies between 10 and 20 keV. Above 20 keV mirrors become very impractical because extremely large mirrors are required to accomplish even minor changes in angles of reflection. The maximum angle of reflection, .theta..sub.max, of photons from a mirror is given by the relation: EQU sin.theta..sub.max =A/E (1)
where "A" is a constant that is a characteristic of the reflecting surface, and "E" is the energy of the photons. For small angles this relation becomes: EQU .theta..sub.max =A/E (2)
If the energy of the incident photons is 20 keV and the reflecting surface is platinum, the maximum angle of reflection is about 0.0030 radians. A parallel beam of photons, 1 cm high, would require a mirror 333 cm (11 ft) long to reflect it and a mirror two to three times as long (22 to 33 ft) to focus it at some reasonable distance. If the photon beam were not parallel but diverging by 0.001 radians, as would be the case for a point source at a distance of 12 m, the mirror would have to be 500 cm long to reflect it and at least 1000 cm (33 ft) long to focus it. If the divergency of the beam were greater than the critical angle (0.0030 radians) then no length of mirror would be long enough to focus the full beam.
Because of this practical limitation, diffraction crystals are more suitable for use at energy levels above 20 keV. Theoretically, the range of energies in which diffraction crystals can be used is limited only at the low end. Diffraction will occur if the Bragg condition for diffraction is satisfied based on the equation: EQU n.lambda.=2d sin .theta.
where "n" is the order of diffraction, ".lambda." is the wavelength of the photons, "d" is the crystalline plane spacing, and ".theta." is the Bragg angle or incident angle. An incident beam will not be diffracted if the wavelength of the beam is longer than twice the distance between the crystalline planes.
The use of bent diffraction crystals has been limited, however, because bending of diffraction crystals has not been easily accomplished. Presently most bent crystals are bent with mechanical forces applied to the surface of the crystal. The bend is almost always only in one plane and compound curves such as spherical and ellipsoidal surfaces are very difficult to obtain (see U.S. Pat. Nos. 2,853,617 issued Sept. 23, 1958 to D. W. Berreman, 4,461,018 issued July 17, 1984 to Ice et al., and 4,737,973 issued Apr. 12, 1988 to Ogawa et al.).
It is an object of this invention to provide a method and apparatus for shaping the surface of a diffraction crystal without mechanical bending.
It is another object of this invention to provide a method and apparatus for controlling the shape of the surface of a diffraction crystal so that the crystal will function as a variable focus crystal diffraction lens.
It is another object of this invention to provide an instrument in which thermal gradients are used to control the shape of the surface of a diffraction crystal.
Additional objects, advantages and novel features of the invention will become apparent to those skilled in the art upon examination of the following and by practice of the invention.